Why can I watch video but not listen to music?
My iPod has been useless for a year or two. It syncs easily, loads everything through itunes very well, even plays movies.
But when I want to listen to music all I get is loud angry static. Sometimes I will get a few seconds of tolerable music, but rarely.
Would it be useful to replace the headphone jack?
That's really strange, but if the sound is fine when watching video, then there shouldn't be anything wrong with the headphone jack.
You could try to format the hard drive to see if that has any effect (check "enable disk use" and apply in iTunes, then use DiskUtility).
But to me it sounds logicboard related, so maybe a cleaning of the logicboard (carefull!!) can solve your problem.